Is sec(α)-cos(α)=sin(α)tan(α) ?

The answer to whether sec(α)-cos(α)=sin(α)tan(α) is True

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prove sec(α)-cos(α)=sin(α)tan(α)

prove

sec (α) - cos (α) = sin (α) tan (α)

True

Solution steps

sec (α) - cos (α) = sin (α) tan (α)

Manipulating left side

sec (α) - cos (α)

Express with sin, cos

= \frac{1 - cos ^{2} ( α )}{cos ( α )}

Manipulating right side

sin (α) tan (α)

Express with sin, cos

= \frac{sin ^{2} ( α )}{cos ( α )}

Rewrite using trig identities

= \frac{1 - cos ^{2} ( α )}{cos ( α )}

We showed that the two sides could take the same form

\Rightarrow True

csc (x) = \frac{1 + sec ( x )}{sin ( x ) + tan ( x )}

tan^{2} (θ) + 6 = sec^{2} (θ) + 5

\frac{cos ( x )}{1 + sin ( x )} + tan (x) = sec (x)

sec (\frac{π}{2} - x) = csc (x)

\frac{1}{csc ( x ) - 1} + \frac{1}{csc ( x ) + 1} = 2 tan (x) sec (x)

Is sec(α)-cos(α)=sin(α)tan(α) ?
The answer to whether sec(α)-cos(α)=sin(α)tan(α) is True